Multiuser Detection in CDMA MIMO Systems with Timing Mismatch

Transcription

1 Multiuser Detectio i CDMA MIMO Systems with Timig Mismatch by Robert Chao Yug Lu A thesis submitted to the Deartmet of Electrical ad Comuter Egieerig i coformity with the requiremets for the degree of Master of Sciece (Egieerig) Quee s Uiversity Kigsto Otario Caada Jauary 2004 Coyright Robert Chao Yug Lu 2004

2 Abstract Today i this iformatio-hugry society Iteret traffic such as multimedia streamig alicatios is drivig the demad for high seed data acet wireless services. The use of multile trasmit ad receive ateas has bee roosed for the fourth geeratio code-divisio multile access (CDMA) wireless cellular etwors i order to meet these demads. Multiuser CDMA multile-iut multile-outut (MIMO) systems have ust recetly bee studied. Receivers roosed for such systems thus far have bee based o the assumtio that erfect owledge of the chael state iformatio is available. Although the effects of chael correlatio ad imerfect estimatio o the MIMO system have bee rigorously studied little or o attetio has bee aid to time-delay mismatch. More imortatly it is well ow that timig estimatio errors i a CDMA system ca result i sigificat erformace degradatio where the ear-far resistat roerty of multiuser detectors is comromised. I this thesis we ivestigate the imact of mismatch i time-delay estimatios betwee trasmit-receive atea airs i a multiuser CDMA MIMO commuicatio system. We first formulate a robust sace-time decorrelator (STD) by decomosig each substream with rectagular chi ulse shaes ito two virtual substreams. A multistage successive iterferece cacellatio (SIC) imlemetatio of the robust ii

3 STD that requires o orderig is the roosed to reduce comlexity ad icrease caacity. The roosed receiver itegrates a receiver diversity combiig rocedure residual error estimatio amlitude averagig ad soft-decisio cacellatio to reduce error roagatio ad oise ehacemet. It is demostrated that the roosed robust sace-time SIC (RSTSIC) achieves sigificat erformace imrovemet over the STD whe delay estimatio error is reset ad its erformace is close to that of the STD with erfect timig estimatio. iii

4 Acowledgemets I am rivileged to have bee a member of the Iformatio Processig ad Commuicatios Laboratory which is a very ositive eviromet for learig ad worig. To this ed I am thaful to all the lab members for the owledge ad friedshi shared. Most imortatly I am grateful to Dr. Steve Blostei for his metorshi. I am fortuate to have had a chace to share his ethusiasm i research; his guidace atiece ad suort are much areciated. I would lie to acowledge the members of my thesis committee Dr. McLae Dr. Alaai Dr. Ibaahla ad Dr. Dia for their ivaluable suggestios ad commets with resect to this thesis. This research is i art suorted by Caadia Istitute for Telecommuicatios Research (CITR) Graduate Awards from Quee s Uiversity Samsug Electroics ad Bell Caada. iv

5 Cotets Abstract Acowledgemets Cotets List of Tables List of Figures List of Symbols List of Abbreviatios ii iv v viii ix xi xv Itroductio. Multiuser Detectio Multile-Iut Multile-Outut Systems Wireless Commuicatios Chael Motivatio Thesis Cotributios Thesis Outlie Bacgroud 0 2. CDMA Multiuser Detectio Otimum Multiuser Detectio Liear MUD v

6 2..3 Multistage Decisio-Drive MUD Multile-Iut Multile-Outut Commuicatio Systems Bell Labs Layered Sace-Time Architecture System Model V-BLAST Detectio Algorithm Multiuser CDMA MIMO Systems System Descritio Multiuser CDMA MIMO Detectors Sace-Time Decorrelator with V-BLAST Hybrid Liear Iterative MUD Layered Sace-Time MUD MCM Detectors that are Robust to Delay Mismatch Predictio Error Aroach Robust MCM Decorrelatig Detector Multistage Robust MCM Decorrelatig Detector Robust MCM SIC Detector Amlitude Averagig ad Soft-Decisio Iterferece Cacellatio Soft-Decisio RSTSIC with Amlitude Averagig Performace Aalysis BER Imlemetatio Comlexity Simulatio Results Sigle-User vs. MCM Detectors i a Multiuser Eviromet Imact of Timig Estimatio Errors vi

7 4.3 Robust to Timig MCM Detectors Performace of the RSTSIC uder Large Delay Variace Sectrally-Efficiet Trasmissio Strategies Sreadig Code Assigmet Varyig the Numbers of Atea Elemets Performace of the RSTSIC with Amlitude Averagig ad Soft- Decisio Fuctio Performace of the RSTSIC uder Zero db Near-Far Ratio Eviromet Coclusios ad Future Wor Coclusios Suggestios for Future Wor Bibliograhy 67 Aedix A 73 Vita 8 vii

8 List of Tables 4. List of MCM receiver acroyms viii

9 List of Figures 2. Geeral bloc diagram of a CDMA multiuser receiver Multistage decisio-feedbac multiuser receiver System bloc diagram of a MIMO V-BLAST system System bloc diagram of a multiuser CDMA MIMO system Samlig of the chi-matched filter resose for rectagular chi ulse. Solid arrows rereset the error i chi-matched filter resose at the samlig oits due to time delay mismatch Decisio fuctios The BER of sigle-user receivers i multiuser eviromet with erfect timig estimatio BER Comariso of STD+VBLAST ad sigle-user V-BLAST receivers i a multiuser eviromet with erfect time estimatio BER of MCM receivers with ad without timig estimatio errors for K = 5 users The BER of sigle-user V-BLAST detector with timig estimatio error i a sigle-user eviromet Performace comariso betwee RSTSIC RSTD ad STD with ad without timig mismatch for K = 5 users ix

10 4.6 Performace of RSTSIC uder various user loads Comariso of aalytical ad simulatio results for K = 5 users The BER as a fuctio of σ T for RSTSIC ad RSTD Comariso of RSTSIC whe usig Gold or radom codes for K = 20 users Performace of the RSTSIC uder various trasmissio strategies for K = 5 users The BER of CMRSIC uder various umber of trasmit ad receive ateas elemets where the umber of users is K = Performace comariso of the RSTSIC emloyig liear or geeralized clier decisio fuctios for K = 5 users The BER of the RSTSIC emloyig geeralized clier decisio fuctio ad amlitude averagig for various user loads The BER as a fuctio of σ T for the RSTSIC with amlitude averagig ad geeralized clier decisio fuctio ad the RSTD. The SNR is set at5 db Performace uder various umber of atea elemets of the CMRSIC with amlitude averagig ad geeralized clier decisio fuctio for K = 5 users Performace comariso of STD ad RSTSIC uder average ear-far ratio of 0 db. K = 5 users x

11 List of Symbols a amlitude of user a amlitude of the th user s th substream a amlitude average at the th iteratio aˆ ( m) amlitude iformatio collected u to the th iteratio a~ ( ) tetative amlitude iformatio collected u to the th iteratio m A amlitude matrix b [i] ith trasmitted bit from user b ( m) data bit of the th user s th substream ˆ ( m) mth bit estimate for user at the th iteratio b bˆ ( m) data bit estimate at the th iteratio for the mth bit of th s users th substream ~ b ( m) tetative bit estimate at the th iteratio for the mth bit of th s users th substream b bˆ b ~ data bit vector data bit estimate vector tetative data bit estimate vector b ˆ( ) data bit vector estimate at the th iteratio xi

12 B (z) feedbac filter c comlex chael coefficiet betwee the th trasmit atea ad the th receive atea c (l) PN code sequece assiged to user at the lth chi c chael vector for the th trasmit atea C C C ~ ~ C ~ C chael matrix N T -by-n T diagoal chael matrix at the th receive atea bloc-diagoal chael matrix of size KMN T -by-kmn T at the th receive atea bloc-diagoal chael matrix of size 2KMN T -by-2kmn T at the th receive atea for RSTD bloc-diagoal chael matrix of size (M+)KN T -by-(m+)kn T at the th receive atea for multistage RSTD C ( ) chael matrix at the th iteratio C ( )' re-ordered chael matrix at the th iteratio d d decisio vector th user s sreadig code vector for the (M+)T S secod iterval d ( ρ i) d right shifted by ( ρ chis i ) L + e error vector e error vector at the th iteratio F(0) F() sectral-factorized lower triagular matrix sectral-factorized uer triagular matrix with zero diagoal G (z) feed-forward filter I N N-by-N idetity matrix K umber of users xii

13 L M sreadig gai frame size (t) AWGN (t) AWGN o receive atea ( i) correlatio betwee AWGN ad sreadig code of ith bit of user ewifo ( ) ormalized outut after MRC m ewifo ( m) matched filter outut at the th iteratio for the mth bit of the th substream of the th user matched filter oise outut AWGN at the th receive atea N R N T umber of receive ateas umber of trasmit ateas (t) rectagular chi ulse of duratio T C r (t) received basebad sigal r (t) received basebad sigal at the th receive atea r r received basebad sigal vector received vector sigal at the th receive atea r stried comosite received sigal at the th iteratio ˆr recostructed received sigal at atea usig oly the extracted iformatio from the th iteratio for the th user s th substream r ( ) received sigal at th iteratio R for CDMA system: cross-correlatio matrix for MCM system: sace-time cross-correlatio matrix R ( ) cross-correlatio matrix at the th iteratio xiii

14 s ( i) th user s sigature waveform for the ith iterval from the th trasmit atea to the th receive atea ˆ i s ( ) estimated sreadig code vector S (t) ormalized sreadig code for user S sreadig code matrix at the th receive atea S sreadig code vector at the th receive atea for RSTD S sreadig code vector at the th receive atea for multistage RSTD S (z) Z-trasform of cross-correlatio matrix T C chi duratio T S symbol duratio w liear detectio trasformatio y (i) ith matched filter outut bit of user y (m) decisio vector for mth bit of user at the th iteratio y matched filter outut vector â amlitude of the error vector at the th iteratio r residual sigal at the th iteratio sˆ i ( ) error sreadig code vector ρ ( mi) sreadig code cross-correlatio betwee mth symbol of user ad ith symbol of user 2 σ τ AWGN variace time delay of the th user xiv

15 List of Abbreviatios AMPS AWGN BER BLAST BPSK CDMA CSI GSM ISI MAI MAP MIMO MCM ML MMSE MRC MUD NFR PIC Advace Mobile Phoe System Additive White Gaussia Noise Bit-Error-Rate Bell Labs layered Sace-Time Biary Phase-Shift Keyed Code Divisio Multile Access Chael State Iformatio Global System for Mobile Iter-Symbol Iterferece Multile Access Iterferece Maximum-A-Priori Multile-Iut Multile-Outut Multiuser CDMA MIMO Maximum Lielihood Miimum Mea-Squared Error Maximal Ratio Combiig Multi-User Detectio Near-Far Ratio Parallel Iterferece Cacellatio xv

16 PN QoS RSTD RSTSIC SIC SINR SISO SNR STD TDMA TD-SCDMA WCDMA ZF Pseudo Noise Quality of Service Robust Sace-Time Decorrelator Robust Sace-Time Successive Iterferece Caceller Successive Iterferece Cacellatio Sigal-to-Iterferece lus Noise Ratio Sigle-Iut Sigle-Outut Sigal-to-Noise Ratio Sace-Time Decorrelator Time Divisio Multile Access Time Divisio Sychroous Code Divisio Multile Access Widebad Code Divisio Multile Access Zero-Forcig xvi

17 Chater Itroductio Wireless commuicatios is oe of the fastest growig idustries i history. Accordig to the Caadia Wireless Telecommuicatios Associatio there are 2 millio mobile hoe users i Caada at the ed of year 2002 reresetig a overall eetratio level of aroximately 37%. It is roected that by the year-ed 2004 more tha half of all Caadias will be mobile hoe users. This lucrative busiess with reveues totallig over $6 billio i 200 i Caada aloe has bee receivig icreasig attetio from both the rivate ad ublic sectors ever sice the first lauch of wireless etwors i the early 980s. The first cellular etwors were based o aalog radio trasmissio techologies such as AMPS (Advace Mobile Phoe System). Busy sigals ad droed calls were frequet as the caacities of these etwors were quicly becomig saturated with icreasig umber of subscribers. The Secod-geeratio digital cellular system was draw u by the idustry to coe with icreased traffic withi a limited amout of badwidth. Oe of these techologies GSM (Global System for Mobile) was itroduced i 99. The ew geeratio of cellular etwor eoyed tremedous success ad was quicly adoted worldwide while aother

18 techology was ust emergig. Qualcomm Ic. itroduced the IS-95 (Iterim Stadard-95) i 993 based o CDMA (code divisio multile access) air-iterface techology as a alterative to GSM. The caacity of CDMA claimed to have roughly 8 times more tha aalog etwors ad 4-6 times that of TDMA (time divisio multile access) the techology used i GSM []. The cellular cocet allows the reuse of the same frequecy bad at differet hysical locatios. Havig a frequecy reuse factor of i.e. every adacet cell is allowed to use the same frequecy bad CDMA rovides the most efficiet use of the radio sectrum. Frequecy laig therefore became obsolete for the CDMA wireless etwor. The secod-geeratio of wireless etwors were maily voice-orieted ad the roliferatio of the Iteret i the mid 990s led the idustry to evisio a etwor that would be caable of deliverig high-seed data acets. The Iteratioal Telecommuicatios Uio adoted three stadards for the third-geeratio (3G) wireless system: CDMA2000 widebad CDMA (WCDMA) ad time divisio sychroous CDMA (TD-SCDMA). The first deloymet of 3G systems aeared i Jaa i 200. Commercially today the CDMA2000 X etwor delivers seeds of u to 2.4 Mbs i the idoor eviromet ad a ea data rate of 53.6 Kbs i the mobile eviromet. The success of the imrovemets i caacity ad data rate of 3G systems ca be attributed to techologies such as smart ateas receiver diversity ad selectable mode vocoder. Aticiatig that the wireless etwors will have similar Iteret usage atters as that of the wired etwors imrovemets to the 3G etwors were actively ursued by the idustry eve before the first commercial 3G etwor was deloyed. The fourth-geeratio wireless etwors are evisioed to rovide ehaced services with high data rate ad itegrated ad coverged services with IP (Iteret rotocol)- 2

19 based seamless etwors [2].. Multiuser Detectio Sread sectrum is a sigal rocessig techique that distiguishes CDMA where a data symbol is modulated with a oise-lie widebad sigal called a seudo-oise (PN) sequece. This rocess is also ow as sreadig ad is iteded to suress multile access iterferece (MAI) due to iterferece from other users i the same cell (itracell-iterferece) ad ossibly users from adacet cells (itercelliterferece). The amout of suressio ossible i the covetioal CDMA receiver a matched filter deeds o the cross-correlatio roerties betwee the PN sequeces from all active users ad the sreadig factor which is defied as the ratio i badwidth betwee the iformatio-bearig sigal ad the PN sequece. Caacity of the system therefore is limited by the available badwidth ad the PN sequece roerties. Whe orthogoal PN sequeces are used however the caacity becomes solely deedet of the sreadig factor. The matched filter is otimal i a white Gaussia oise eviromet but suffers from the ear-far effect whe MAI is reset: the erformace of the matched filter deteriorates whe the received owers from iterferig users are greater tha that of the desired user. Striget ower-cotrol is required to avoid the ear-far roblem but it is a difficult tas i ractice. Multiuser detectio or MUD sees to overcome the iheret shortcomigs of covetioal CDMA receivers by rovidig ear-far resistace for the receiver i the rocess of elimiatig the MAI. A otimum maximum lielihood (ML) MUD receiver was roosed by Verdú [3]. The ML multiuser receiver ecomasses a ba 3

20 of matched filters that roduces a set of sufficiet statistics followed by a Viterbi decoder. The comlexity of the ML receiver is exoetial i the umber of users rederig it imractical. Subotimum liear receivers such as the decorrelatig ad the miimum mea-squared error (MMSE) receivers have bee roosed to trade off comlexity ad erformace amog the covetioal ad otimal receivers [4] [5] however they still require comutatioally itesive matrix iversio. More ractical ad simle aroaches iclude multistage decisio-feedbac receivers such as the arallel iterferece cacellatio (PIC) detector [6] as well as the serial iterferece cacellatio (SIC) detector [7]. Although both receivers have comlexity liear i the umber of users the SIC causes loger delay while the PIC demads more hardware. All of the above-metioed multiuser detectors have assumed that the exact sigal time-delays of all active users i the same cell are ow which is imossible i ractice. Several well-ow time delay estimators such as the slidig correlatio delay estimator [8] subsace-based estimator [9] [0] ad others i []-[4] all rovide estimatio to withi 20% of the sreadig chi iterval or better. Perfect timig estimatio however caot be achieved as oise ad MAI hiders estimatio accuracy. The erformaces of multiuser detectors uder time-delay estimatio errors or timig mismatch have bee studied i [5]-[2]. It is show that multiuser receivers uder timig mismatch are o loger ear-far resistat ad uder mismatch MUD receiver erformaces ca eve be worse tha that of the matched filter. Thus ew techiques have bee roosed to mitigate the devastatig effects of timig mismatch i MUD [22]-[25]. The decorrelatig-based detectors i [22] ad [23] effectively double the umber of users causig icreased oise ehacemet. As a result it is show by aalysis that the caacity of these decorrelatig receivers is reduced by 50%. Both MMSE-based receivers i [22] ad [24] are based o 4

21 stochastic delay modellig ad both imrove the average bit-error-rate (BER) but caot comletely elimiate the MAI itroduced by timig mismatch ad therefore are ot ear-far resistat. The robust SIC roosed by Zha ad Blostei [25] is show to be ear-far resistat. Furthermore the robust SIC has the advatage that the caacity ca surass 50% of the sreadig gai ad is of comlexity liear i the umber of users..2 Multile-Iut Multile-Outut Systems With icreasig demads o curret wireless systems ut forth by high-seed acet data ad multimedia streamig services techologies that will deliver icreased caacity have bee of iterest to researchers i recet years. While a vast literature is available o icreasig user data rate through techiques such as multicode ad variable sreadig gai they do so at the exese of reducig the total system throughut. A true high-seed multiuser wireless system ca oly be achieved through a icrease i system sectral efficiecy measured i bits er secod er Hertz er sector. The wireless multile-iut multile-outut (MIMO) commuicatio systems see to achieve caacities that are close to the Shao limit by emloyig multile trasmit ad receive ateas as well as advaced sace-time sigal rocessig techiques. I the ast receiver diversity has bee used to mitigate the detrimetal effects of multiath fadig. Atea elemets at the receiver are saced sufficietly far aart such that the sigal received at each atea ca be viewed as havig roagated through ideedet fadig chaels. Each ath has a distict ad time-varyig amlitude hase ad agle of arrival. The received sigals are the combied usig 5

22 otimal weights formig a sigal with better quality tha each idividual oe. Three commo diversity schemes are maximum ratio combiig (MRC) equal gai combiig (ECG) ad selectio combiig (SC). Recetly icreasig research efforts have bee focused o satial diversity otios for both the mobiles ad basestatio. With curret 3G cellular systems usig 2.4 GHz ad 5 GHz carrier frequecies mobiles will be able to carry multile ateas with sufficiet sacig without havig to icrease their size sigificatly. Various MIMO schemes are curretly uder cosideratio for 4G wireless commuicatio systems. Oe of the most romisig sace-time rocessig techiques is the Bell Labs Layered Sace-Time (BLAST) system roosed by Fochii [26]. I a rich scatterig chael the multile ateas form i effect multile sigle-iut sigle-outut (SISO) chaels sice each satial multilexed ath fades ideedetly from oe aother. The caacity of the BLAST architecture therefore icreases liearly with the umber of satial multilexed aths formed..3 Wireless Commuicatios Chael Ay commuicatios system i the mobile radio chael suffers from a time-varyig chael heomeo ow as multiath fadig. The time-variat imulse resose of the chael is a cosequece of the costatly chagig hysical characteristics of the media. The chael is said to be frequecy-oselective if the sigal badwidth is much smaller tha the coherece badwidth of the chael. Uder such a sceario the chael has costat gai ad liear hase over the trasmitted sigal badwidth. The received sigal is therefore simly the trasmitted sigal multilied by a 6

23 comlex-valued time-varyig chael coefficiet. Sice all received multiath comoets udergo the same atteuatio ad hase shift they are ot resolvable. The chael gais ca be modeled as comlex Gaussia radom variables with zero mea i a Rayleigh fadig eviromet where there is sufficiet local scattererig. Ricea fadig occurs whe there exists a lie-of-sight betwee the trasmitter ad receiver ad the chael gais ca be modeled as comlex Gaussia radom variables with o-zero mea. The trasmitted sigal is subected to differet chael gais ad hase shifts across the frequecy bad if the sigal badwidth is larger tha the coherece badwidth of the chael. I such a case the chael is said to be frequecyselective. I the time domai frequecy-selectivity occurs whe the sigallig eriod is smaller tha the multiath delay sread of the chael. Multile relicas of the trasmitted sigal each with differet amlitude ad delay arrive at the receiver ad cause iter-symbol iterferece. I this case the received multiath sigals are resolvable ad the umber of resolvable sigal comoets is the roduct of the sigal badwidth ad the multiath delay sread of the chael. The raidity of the fadig is determied by the coherece time which is a statistical measure of the time eriod over which the chael imulse resose is essetially time-ivariat. If the symbol duratio is smaller tha the coherece time of the chael the chael atteuatio ad hase shift are essetially fixed for the duratio of at least oe sigallig iterval. Whe this coditio holds the chael is referred to as slow fadig chael. Otherwise the chael resose chages raidly durig the symbol eriod ad is termed fast fadig. 7

24 .4 Motivatio Wireless MIMO systems have bee traditioally studied i oit-to-oit commuicatios where exchage of iformatio ivolve oly a sigle air of trasmit ad receive termials. However with sace-time rocessig techiques beig cosidered for use i 4G cellular wireless commuicatio systems researchers have begu exlorig various multicast systems ivolvig the MIMO aradigm [27]- [29]. By combiig a CDMA system equied with MUD that is ear-far resistat with a sectrally-efficiet MIMO system the resultig multiuser CDMA MIMO (MCM) system offers otetially romisig high-seed commuicatios for 4G cellular wireless etwors. Curret state-of-the-art MCM receivers utilize comutatioally-itesive rocessig techiques such as BLAST decorrelatig ad re-whiteig. These MCM receivers also assume erfect estimatio of chael state iformatio (CSI). While ideal chael coditios ad favourable assumtios lead to imressive erformaces estimatio errors result i o-ideal receiver erformace. Timig mismatch a source of erformace degradatio for CDMA systems has ot bee thouroughly ivestigated i the BLAST research literature. Furthermore i MCM wireless systems ad to the best of our owledge o research has bee doe o the imact of timig estimatio errors for the time-delays betwee each trasmit-receive atea air..4 Thesis Cotributios The rimary cotributios of this thesis are briefly summarized as follows: This thesis ivestigates a more realistic model that taes ito cosideratio 8

25 mismatch i time-delay estimatio betwee trasmit-receive atea airs. Time-delay mismatch will be show to cause severe erformace degradatio to receivers that assume erfect timig. A ovel sace-time SIC that is robust to timig mismatch is roosed i this thesis. The robust sace-time SIC (RSTSIC) receiver utilizes receiver diversity by combiig the received sigals from each atea usig otimum weights. I additio amlitude averagig ad soft-decisio iterferece cacellatio rocedures are imlemeted to mitigate oise ehacemet ad error-roagatio. The RSTSIC is show to have erformace very close to that of the sacetime decorrelator with erfect time-delay iformatio. Moreover RSTSIC erformace is show to be isesitive to large time-delay estimatio errors. Comlexity is show to be liear i the umber of users ateas ad bits trasmitted er frame. I the case of a MCM system uder timig mismatch ideedet fadig ad wide agle sread scatterig it is foud that radom codes are ot suitable for sreadig to combat multile-access iterferece itroduced by the multile trasmit ateas. It is foud istead that the same Gold code may be effectively used to sread all data substreams of a user to maximize system caacity..5 Thesis Outlie Chater 2 of this thesis begis with a overview of multiuser detectio. The discrete basebad model is itroduced followed by a brief itroductio to the covetioal 9

26 CDMA receiver ad the otimum multiuser detector. Liear ad multistage subotimum multiuser receivers are the described. The last subsectios of this chater exlai the theory trasmissio scheme ad detectio algorithms of a wireless MIMO commuicatios system. I Chater 3 we reset a MCM system model where trasmissio scheme ad chael assumtios are described. Next a survey of the curret state-of-the-art MCM receivers is reseted followed by the formulatio of the roosed robust sace-time SIC. The cocet of soft-decisio fuctios is discussed ad the geeralized clier decisio fuctio is the alied to the RSTSIC algorithm alog with amlitude averagig. Fially the BER ad comutatio comlexity of the RSTSIC are briefly aalysed. Havig laid the groudwor i the revious chaters we erform comuter simulatios i Chater 4. We first ivestigate sigle-user MIMO receiver erformace uder a multiuser eviromet. The imact of timig error o the erformace of existig MCM receivers are studied ad comared to the roosed RSTSIC. We the more thoroughly examie roerties ad erformaces of the RSTSIC uder various coditios. The chater eds with a discussio o sectrallyefficiet trasmissio strategies. Chater 5 cocludes this thesis ad rovides several suggestios for future wor. 0

27 Chater 2 Bacgroud I this chater we review the basic attributes of MUD ad MIMO systems. Various otimum ad subotimum multiuser receivers are first reseted as well as discussios of their advatages ad disadvatages. I Sectio 2.2 a classic wireless MIMO commuicatios model ad its detectio algorithms are described. 2. CDMA Multiuser Detectio I cellular CDMA systems erformace is limited by iterferece from co-chael users or MAI. The advet of MUD i the late 980s brought o a whole ew horizo for cellular etwors as striget ower cotrol became o loger ecessary. However ew techological challeges arise eve for today s real-time digital sigal rocessors as the ew receivers exhibit high comutatioal comlexity ad latecy. I this subsectio we itroduce the imortat sigal rocessig techiques used i the covetioal ad otimal receivers as well as subotimal receivers roosed subsequetly that attemt to balace the trade off betwee comlexity ad erformace.

28 2.. Otimum Multiuser Detectio Cosider a asychroous CDMA system with K users sharig a additive white Gaussia oise (AWGN) multile-access chael. Assumig a quasi-static chael the amlitude ad timig delay of each user ca be cosidered as costats durig the trasmissio i a frame of M bits which are biary hase-shift eyed (BPSK) modulated. The received sigal after dow-coversio to basebad therefore is where K M r( t) = a b [ i] S ( t it τ ) + ( t) (2.) = i= S L S ( t its ) = l= 0 c ( l + il) ( t lt C it S ) S ( t) [0 T ) S (2.2) S (t) is the determiistic sigature waveform for user ormalized to have uit eergy (t) is a rectagular ulse of duratio [0Tc) 2 * S = S ( t) S ( t) dt = (2.3) c ( l) { } is the PN code sequece assiged to the th user T S L = is the legth of PN code sequece T C T S is the symbol iterval T C is the chi iterval a is the received amlitude of the th user s sigal b [ i] { } is the BPSK modulated ith raw data bit trasmitted by the th user τ is the time delay of user where it is assumed that 0 τ < T S (t) is the white Gaussia oise with ower sectral desity 2 σ 2

29 Throughout this thesis ( ) * cougate trasose oeratios resectively. T ( ) ad ( ) H deote the cougate trasose ad Fig. 2. deicts a bloc diagram of a CDMA multiuser detector. The receiver frot-ed ca be idetical for both the covetioal sigle-user detector ad multiuser detectors ad cosists of a ba of matched filters each matched to a articular user s PN sequece. The oututs of the ba of K matched filters are the samled at the symbol rate ad ca be exressed as (i) y = = + = + + ( i+ ) TS + τ its + τ ( t) S m= ( t) S r( t) S K M m = = ( t it = m= = a b [ i] + M K ( t it ( t it a b [ m] S a b [ m] S K M S S τ ) dt ( t mt a b [ m] S τ ) dt M = m= S τ ) dt ( t mt where the first term is the result of Equatio (2.3) S τ ) S S ( t mt τ ) S ( t it τ ) S ρ( mi) + ( i) S ( t it S S τ ) dt ( t it τ ) dt S τ ) dt (2.4) ρ ( mi) = S ( t mt τ ) S ( t it τ dt ad S S ) ( i) = ( t) S ( t it τ ) dt. From Equatio (2.4) we see that the matched S filter outut y (i) is comosed of three terms: the desired iformatio a b [i] the MAI ρ( mi) ad the oise ( i). Collectively the matched filter oututs for all K users ad M symbols ca be exressed i a log vector as y T T T = [ y () K y ( M )] (2.5) where 3

30 Matched Filter User Syc y (i) b [ ] ˆ i Matched Filter User 2 Syc 2 y 2 (i) Multiuser Detectio b [ ] ˆ2 i r(t) Algorithm Matched Filter User K Syc K y K (i) ˆ [ i] b K Figure 2.. Geeral bloc diagram of a CDMA multiuser receiver ( i ) = [ y( i) K y K ( i) ] T y (2.6) is the matched filter outut vector for K users i the ith symbol eriod. The covetioal sigle-user detector erforms symbol estimatio directly ad ideedetly o each of the y (i) matched filter oututs treatig the MAI as white oise. Matched filterig relies solely o the sigal costellatio ad PN code assigmet to reduce MAI caused by PN sequece crosscorrelatios. This detectio method is otimum i the sigle-user case or if all user PN code sequeces are mutually orthogoal. The matched filter receiver wors reasoably well i a multiuser eviromet if there are few users with low correlatio sequeces ad the received owers from differet users are early equal. However i mobile wireless eviromets the receiver suffers from dee fadig ad the ear-far effect where iterferig users owers are much greater tha the desired user which reders the covetioal detector useless. I additio orthogoality betwee the PN sequeces ca be destroyed by multiath sigal roagatio. Thus usig a covetioal 4

31 receiver MAI is severe ad the erformace is very oor for ucoded wireless systems. Util the mid 980 s the matched filter was regarded as the otimum CDMA receiver ad system limitatios such as the ear-far effect were regarded as a iheret limitatio of the CDMA system. I 986 Verdú roved that the ear-far roblem is ot a iheret limitatio of CDMA itself but of the matched filter receiver [3]. Verdú formulated a multiuser receiver based o the maximum-lielihood (ML) criteria which is equivalet to the otimum maximum a riori (MAP) criteria whe the trasmitted sequeces are equirobable. The roosed receiver cosists of a frot-ed matched filter ba followed by a Viterbi forward dyamic rogrammig detectio algorithm that selects the sequece b that maximizes the coditioal robability P [{ r( t) t R} b]. The matched filter outut vector y rovides sufficiet statistics for otimum detectio. I [3] a otimum miimum-robability-of-error detector is also roosed usig the same frot-ed matched filter ba followed by a bacward-forward dyamic rogrammig detectio algorithm. These receivers attai essetially sigle-user erformace with the assumtio that timig amlitude ad sigature waveforms of all the active users are all ow. Although the otimum detectors sigificatly outerform the covetioal detector they do so at the exese of icreased comlexity that is exoetial i the umber of users i the system Liear MUD The disarity i comlexity ad erformace betwee the covetioal detector ad otimum multiuser detectors motivated researchers to see subotimum alteratives that exhibit better erformace/comlexity tradeoffs. A grou of liear multiuser detectors that are geeralizatios of sigle-user itersymbol iterferece (ISI) chael 5

32 equalizer couterarts are formulated i [4] ad [5]. As see i Fig. 2. liear multiuser detectors erform liear trasformatios o the matched filter outut y which ca be exressed as y = RAb + (2.7) where the zero-mea Gaussia oise vector has the MKxMK covariace matrix 2 σ R R(0) R() R = 0 M 0 R( ) R(0) R() L 0 R( ) R(0) O 0 L O O R() 0 M 0 R( ) R(0) (2.8) A = diag a ()... a ()... a ( M )... a ( )} (2.9) { K K M T b = [ b () b K () b(m) b K (M)] (2.0) The ( ) th elemet of the KxK sigal correlatio matrix R(m) is: ( m) S ( t τ ) S ( t + mts τ ) R = dt (2.) ad R (m) has the followig roerties vector is R( m) R( m) = 0 T = R m > ( m) Let w be a liear trasformatio vector for the multiuser detector. The decisio T d = w y (2.2) The decorrelatig detector i [4] has a liear trasformatio equivalet to the iverse of the correlatio matrix The decisio vector is the w = R (2.3) 6

33 d = R ( RAb + ) = Ab + R (2.4) ad sice BPSK is used the bit decisio is determied by the sig of the decisio vector bˆ = sig( d) (2.5) The decorrelator ca be viewed as a modified matched filter orthogoal to the MAI ad similar to the zero-forcig (ZF) equalizer. This receiver has quadratic comlexity i the umber of users ad is otimum i three seses: ear-far resistat leastsquares ad ML whe the received amlitudes are uow [4]. A multiuser detector is said to be ear-far resistat if its asymtotic multiuser efficiecy is ozero over all ossible received eergies of all other users where asymtotic multiuser efficiecy quatifies the erformace loss due to the existece of other users i the chael [44]. The decorrelator receiver has the advatage that owledge of the received amlitudes is ot required. However the iversio of the chael erformed by the decorrelator ehaces the bacgroud oise give by the oise vector R - i equatio (2.4). The decisio vector has covariace matrix H 2 E [( R )( R ) ] = σ R (2.6) which ca results i oise ower ehacemet creatig a ga betwee the sigle-user error erformace ad the decorrelator error robability. Aother liear detector with the same structure is roosed i [5] based o the otimizatio of the miimum mea-squared error (MMSE) criteria: The solutio to the above equatio is T w = mi E [( b bˆ) ( b bˆ)] (2.7) w w = ( R + ( A A) ) 2 T σ (2.8) 7

34 While the sigle-user matched filter combats white oise exclusively ad the decorrelator elimiates MAI disregardig bacgroud oise the MMSE liear detector forms a comromise betwee the two taig the relevat imortace of the bacgroud oise ad iterferig users ito accout. I fact the decorrelator ad covetioal detectors are limitig cases of the MMSE liear detector: the MMSE detector erformace aroaches that of the covetioal detector as the bacgroud oise variace goes to ifiity ad that of the decorrelator as the bacgroud oise variace goes to zero. Therefore the MMSE liear detector also achieves the same otimum ear-far resistace as that of the decorrelator Multistage Decisio-Drive MUD A umber of differet o-liear multiuser detectio strategies i multiuser detectio have bee roosed based o multistage ad decisio feedbac rocessig. Oe simle ad atural idea the multistage SIC was roosed i [6]. I SIC the strogest user is detected first usig a covetioal matched-filter igorig all other users with smaller eergies; this requires the detector to order the users accordig to sigal stregth. Assumig hard decisios are emloyed the th stage bit estimate of the th user is ˆ b ( m) = sig[ y ( m)] (2.9) where y ( m) = y ( m) 0 K l= + ˆ R ()ˆ b ( m ) R (0) b ( m) R ( ) bˆ ( m + ) (2.20) l l l l l l= l + l ad the iitial bit estimate ca be obtaied by the covetioal matched filter outut ˆ 0 b ( m) = sig[ y ( m)] (2.2) 8

35 The SIC receiver recostructs the sigal usig the bit estimate (2.9) ad subtracts it from the comosite received sigal. This will cacel the iterferig sigal rovided that the decisio was correct ad that the receiver has accurate amlitude ad timig iformatio. The iitial bit ad outut estimates of the detector ca be imroved by usig other subotimum schemes such as a decorrelatig first stage deedig o the comlexity oe is able to tolerate. The SIC has the advatage that its comlexity is liear i the umber of active users ad very little comutatio is required relative to the liear detectors. Desite its simle structure a shortcomig of the SIC is that ay errors i amlitude estimatio ad itermediate decisios will traslate directly ito oise or MAI for future decisios. This roblem ca be mitigated by usig soft itermediate decisios or weighted sigal cacellatio accordig to each user s ower level: strog users are much more reliable ad are subtracted with more weight while oly small roortios of wea users sigals are stried away. Whe a liear decisio fuctio is emloyed the liear SIC is show to corresod to alyig Gauss-Seidel iteratio to aroximate matrix iversio [32] ad thus ower-orderig is ot required. A sigle-stage decisio-feedbac detector is studied i [30]. The detector show i Fig. 2.2 cosists of a feed-forward filter fed by matched filter oututs ad a feedbac filter fed by ast decisios. Uder the white oise model the otimum decorrelatig decisio-feedbac detector tries to maximize the SNR at the decisio device ad the filters are obtaied through sectral factorizatio. The discrete model i Equatio (2.7) ca be rereseted i the z-trasform domai as y ( z) = S( z) Ab + ( z) (2.22) where T S ( z) = R () z + R(0) + R() z (2.23) 9

36 Matched Filter User Syc b [ ] ˆ i Matched Filter User 2 Syc 2 G(z) b ˆ2[ i] r(t) Matched Filter User K Syc K ˆ [ i] b K B(z)A Figure 2.2. Multistage decisio-feedbac multiuser receiver is ideedet Gaussia with covariace ad ca be factored as T T ( z) = ( F (0) + F () z) (2.24) σ 2 I R(m) is defied i Equatio (2.) T T R( 0) = F (0) F(0) + F () F() (2.25) T R( ) = F (0) F() (2.26) where F(0) is lower triagular ad F() is uer triagular with zero diagoal. From (2.25) ad (2.26) the matrix S(z) ca rereseted by T S ( z) = [ F(0) + F() z] [ F(0) + F() z ] (2.27) The bit estimate of the asychroous decorrelatig decisio-feedbac receiver is show to be bˆ = sig[ G( z) y( z) B( z) Abˆ] (2.28) 20

37 where T G ( z) = [ F(0) + F() z] (2.29) B ( z) = F(0) diagf(0) + F() z (2.30) The otimal feed-forward filter G(z) is derived to be the oise whiteig filter that cacels MAI for those bits that have ot yet bee detected while the feedbac filter B(z) attemts to elimiate MAI by regeeratig ad cacellig the iterferig sigals from the detected bits. The feedbac filter ca tae advatage of its causal structure by demodulatig users i the order of decreasig eergy so that the decisios made for the stroger users ca be utilized by the weaer users. The decisio-feedbac detector is iheretly more comlex tha other decisiodrive couterarts due to the eed for erformig a sectral decomositio i obtaiig the filter coefficiets. However the filter coefficiets ca be adatively udated for each symbol iterval ad a MMSE decisio-feedbac detector is roosed i [3] by the same author. 2.2 Multile Iut Multile Outut Commuicatio Systems I order to suort high-seed Iteret alicatios while esurig the quality of service (QoS) the sectral efficiecies of the ext geeratio of wireless etwors has to be greatly ehaced. The cocet of multile-iut multile-outut (MIMO) systems itroduced i the mid 990s demostrated that usig multile atea elemets at both the receiver ad the trasmitter ca result i eormous caacity gais [26] [46]. Sice the various MIMO architectures have bee roosed such as sace-time bloc codig [34] [47] ad smart atea beamformig [48]. I this 2

38 chater we shall focus o a early ad well-ow high-rate MIMO architecture ow as the Bell Labs Layered Sace-Time system Bell Labs Layered Sace-Time Architecture The BLAST is a arrowbad oit-to-oit commuicatio architecture for achievig high sectral efficiecy. The diagoally-layered sace-time architecture ow ow as diagoal BLAST or D-BLAST is roosed by Foschii [26]. It uses multile ateas at both the trasmitter ad receiver ad a codec architecture that diserses the coded blocs across the diagoals i sace-time. I a rich Rayleigh scatterig eviromet this codec structure has caacity that icreases liearly with the umber of atea elemets u to 90% of the Shao theoretical caacity limit. However D-BLAST suffers from high imlemetatio comlexity ad a simlified codig techique vertical BLAST or V-BLAST is roosed i [33]. The essetial differece betwee D-BLAST ad V-BLAST lies i their resective trasmissio codig rocesses. I D-BLAST temoral redudacy is itroduced betwee the substreams by disersig the code blocs alog the sace-time diagoals. I V-BLAST however the ecodig rocess is simly a demultilexig oeratio. The iter-substream bloc codig techique is what leads to D-BLAST s higher sectral efficiecy. For a large umber of ateas D-BLAST ca offer at most 30% icrease i caacity over V- BLAST. The receiver rocessig for V-BLAST is much simlified over D-BLAST however sice the ullig ad cacellatio detectio algorithm does ot exted across the temoral domai. A high-level bloc diagram of a V-BLAST system is show i Fig Cosider a oit-to-oit system where the umber of trasmit ateas is N T ad the umber of receive ateas is N R. A sigle bit stream is demultilexed ito several 22

39 Tx Rx Tx 2 Rx 2 Data Stream :N T DEMUX Quasistatic Rayleigh fadig chael V-BLAST receiver Estimated data Tx N T Rx N R Figure 2.3. System bloc diagram of a MIMO V-BLAST system substreams ad each substream is the modulated ideedetly ad set through a searate trasmit atea. If we assume ideal Rayleigh roagatio the chael betwee each trasmit ad receive atea air ca be characterized by a comlex Gaussia amlitude coefficiet. Therefore the sigal received from each substream ca be rereseted by a comlex vector with dimesio N R modulated by its data symbol ad the total received sigal is the sum of the sigals received from each of the N T substreams ad Gaussia oise. Note that we ca thi of the comlex N R - vector for each substream as a comlex satial-sreadig code. Moreover if N R is equal or greater tha N T ad there is rich scatterig i the chael such that the substream chael vectors are ideedet oe ca use the V-BLAST detectio algorithm to demodulate the substream based oly o the satial characteristics formed by the atea array. 23

40 2.2.2 System Model At the trasmitter a sigle data stream is demultilexed ito N T substreams ad each substream is the ecoded ideedetly ito symbols ad fed to its resective trasmitter. Trasmitters :N T are themselves ordiary BPSK trasmitters ad they oerate co-chael at symbol rate /T S symbols/sec with sychroized symbol timig. The wireless chael is assumed to be quasi-static flat fadig ad rich scatterig. The comlex fadig coefficiets betwee each atea air are assumed to be ideedet ad have bee estimated at the receiver by a short traiig sequece rior to the detectio rocedure. I the followig we tae a discrete-time comlex basebad view of the system model for a sigle trasmitted vector symbol assumig symbol-sychroous receiver samlig ad erfect timig estimatio. After matched filterig ad symbol rate samlig we ca rereset the received sigals at the N R receive ateas as: T r = [ r r2 K r NT ] (2.3) The trasmitted vector symbols from N T trasmit ateas ca also be orgaized ito vector form: T b = [ b b2 K b NT ] (2.32) Therefore the received sigal ca be exressed as a liear combiatio of the trasmitted sigal b: r = Cb + (2.33) where C is the N R -by-n T comlex chael matrix ad is the comlex AWGN with satially ad temorally white comoets of idetical ower receivers. 2 σ at each of the N R Due to a assumed rich-scatterig eviromet the elemets of the matrix C are 24

41 outcomes of ideedetly ad idetically distributed (i.i.d.) comlex Gaussia variables of uit variace. The chael matrix ca be artitioed ito colums corresodig to the N T trasmitted sigals: C = (2.34) T [ c c 2 K c N T ] V-BLAST Detectio Algorithm Here we describe the techique for symbol detectio i V-BLAST first roosed i [33]. Taig advatage of the iheret timig sychroism i the system model ordered SIC is used alog with liear ullig to erform symbol detectios. The criterio of SIC orderig i the V-BLAST algorithm is based o the maximizatio of ost-detectio sigal-to-iterferece lus oise ratio (SINR). It is show that this method of orderig is ideed globally otimal. The ZF criterio is chose for the ullig rocess to simlify the algorithm descritio although the MMSE criterio ca be alied i a similar rocess. Let idex the iteratio where N T Ste (): Calculate the iverse of the correlatio matrix formed from the chael: R ( ) Re[ C ( ) C( )] H = Ste (2): Fid the substream g whose ost-decorrelator SNR is the highest corresodig to the miimum amog the first N T -+ diagoal etries of R ( ) : g = arg mi[ R ( ) ( g g ) ] g =... N T + The ullig vector w is the gth row of R ( ) gth substream is: b ˆ( ) = sig( wr( )) ad the bit estimate of the 25

42 Ste (3): Perform iterferece cacellatio by subtractig the detected sigal from the received sigal: r( + ) = r( ) c gb ˆ( ) Reorder C ( ) such that the gth colum ad the last colum are iterchaged: C ( )' = [ c K c K c N c g ] = [ C( + ) c g ] T where C ( +) is defied as C ( )' with the last colum c g deleted. Ste (4): Go bac to Ste icremet ad reeat util all N T substreams have bee detected. The V-BLAST caacity has bee show to grow liearly with the umber of ateas. For large SNR if a otimum umber of N ot trasmit ateas are used the for each 3 db codig gai the beefit is roughly a additioal N ot bits/s/hz. Imairmets such as timig error hase oise carrier frequecy offset ad imerfect chael estimate ca cause sigificat system erformace degradatio. Furthermore o-ideal chael coditios such as multiath fast fadig ad correlatio will also have large egative imact o erformace of the system. 26

43 Chater 3 Multiuser CDMA MIMO Systems The ever-icreasig demad o wireless commuicatios today has led to a tremedous eed a greater sectral-efficiecy. Therefore a sigificat focus of late has bee to develo systems that offer both high caacity such as that of V-BLAST alog with MAI resistace esecially i the dowli (from basestatio to mobile). Give the eormous otetial of multiuser CDMA MIMO (MCM) systems researchers have recetly begu to ivestigate the ossible caacity ad bit error rate (BER) erformace of such systems [27]-[29]. I this chater we reset a dowli model of the MCM system followed by a overview of curret state-of-the-art MCM receivers. We will the roose several robust MCM receivers leadig to the formulatio of the robust sace-time SIC (RSTSIC). Amlitude averagig ad the geeralized clier decisio fuctio are the icororated ito the RSTSIC. Fially erformace ad comlexity are aalyzed. 3. System Descritio We cosider the dowli receiver that has owledge of the sigature waveforms for all users. While a similar model aears i [27] there have bee few treatmets of 27

44 Rx Tx Rx N R MCM Detector data User PN Code Mobile Tx 2 User 2 PN Code 2 SRC DEMUX User K PN Code K Base Statio Tx N T Rx N R Rx MCM Detector Mobile K data Figure 3.. System bloc diagram of a multiuser CDMA MIMO system MCM systems i the literature. To date the issue of timig error effects have ot bee addressed. The system cosists of K users each equied with N R receive ateas to demodulate N T ideedet data substreams trasmitted from a sigle basestatio with N T ateas. Figure 3. shows the geeral bloc diagram of the roosed system. The KN T data substreams are each sread by a legth L sreadig code ad the trasmitted through a rich-scatterig chael. Ateas are assumed to be far eough aart such that the comlex fadig coefficiets amog the ateas are ucorrelated. It is assumed that time delays betwee atea airs are ideedet ad are restricted to lay withi oe symbol iterval. To focus o timig errors edge effects [37] are elimiated by usig a isolatio bit isertio receiver [38]. By isertig a bla bit iterval after every M bit itervals ad selectig the received sigal of legth M+ symbols the iterferece from the ext frame is effectively 28

45 bloced from the curret oe. For clarity ad brevity we cosider oly sigle-ath chaels. However the model ad methods reseted here ca be exteded to the case of multiath chaels i a straight-forward maer. The coheretly received comlex basebad sigal for a frame of M data bits at the th (=... N R ) atea is M N K T r ( t) = c a s ( t mt τ ) b ( m) + ( t) (3.) m= = = s where c is the comlex chael coefficiet betwee the th trasmit atea ad the th receive atea a is the amlitude of the th user s th substream s (t) is the ormalized PN code sequece of the th user T s is the symbol iterval τ is the time delay of the ath betwee the th trasmit atea ad the th receive atea b ( m) is the BPSK modulated data symbol of the th user s th substream ad (t) is the AWGN o receive atea. The chael amlitudes are ideedet zero-mea comlex Gaussia variables with uit variace 2 = I (3.2) N T N R E( c c ) 2 where I N deotes a idetity matrix of size N ( ) deotes the comlex cougate. After chi matched filterig ad chi rate samlig the discrete-time comlex basebad received sigal from (3.) at its th atea for a frame of M data bits ca be writte as a comlex (M+)L-vector ~ r = S C Ab + (3.3) where S = S () S (2) L S ( )] (3.4) [ M is the real (M+)L-by-KMN T sreadig code matrix formed from cocateatig the matrices 29